I find the typical thought experiment of "picture an apple" less illustrative than something like "picture the face of a co-worker you see every day but aren't friends with and tell me the color of their eyes." In the apple case, everyone has a "concept" of apple and an experience of "thinking about an apple"---the difference is really in what you can deduce from that thinking and how, if that make sense. Are you reasoning on the basis of an image or from more or less linguistic facts ("apples are red therefore..." etc)?
The main difference that's more than an "implementation" detail of how you think, so to speak, but really a limit concerns what's called "episodic memory." People with aphantasia rather singularly cannot re-experience the emotions of past experiences. There are a lot of studies on this and I can look up the references if you're interested.
When I was really trying to make sense of my own aphantasia, I found https://www.hurlburt.faculty.unlv.edu/codebook.html to be one of the most fascinating resources: it's essentially a catalog of all the different modalities of inner experience a large study found. Probably there are critiques of his methodology etc, but regardless it's an invaluable aid for trying to figure out how exactly you think.
It's hard to write about these things...
I am mostly aphantasaic, but have no trouble at all remembering emotions.
The connection of aphantasia to strongly deficient autobiographical memory (SDAM) is well-attested now. You can find numerous clinical studies on the matter.